The Beer-Lambert law, also known as Beer's law relates the absorption of light to the properties of the material through which the light is traveling. The law states that there is a logarithmic dependence between the transmission (or transmissivity), T, of light through a substance and the product of the absorption coefficient of the substance, α (α′), and the distance the light travels through the material (i.e. the path length), l. The absorption coefficient can, in turn, be written as a product of either a molar absorptivity (extinction coefficient) of the absorber, ε, and the concentration c of absorbing species in the material, or an absorption cross section, σ, and the (number) density N of absorbers.
For liquids, these relations are usually written as
  T  =            I              I        0              =                  10                              -            α                    ⁢                                          ⁢          l                    =              10                              -            ɛ                    ⁢                                          ⁢          lc                    
whereas for gases, and in particular among physicists and for spectroscopy and spectrophotometry, they are normally written
  T  =            I              I        0              =                  10                              -                          α              ′                                ⁢          l                    =              10                              -            σ                    ⁢                                          ⁢          lc                    
where I0 and I are the intensity (or power) of the incident light and the light after passing through the material, respectively. The transmission (or transmissivity) is expressed in terms of an absorbance which for liquids is defined as
  A  =      -                  log        10            ⁡              (                  I                      I            0                          )            
whereas for gases, it is usually defined as
      A    ′    =      -          ln      ⁡              (                  I                      I            0                          )            
This implies that the absorbance becomes linear with the concentration (or number density of absorbers) according toA=εlc=αlandA=σlN=α′l
for the two cases, respectively.
Thus, if the path length and the molar absorptivity (or the absorption cross section) are known and the absorbance is measured, the concentration of the substance (or the number density of absorbers) can be deduced.
A conventional photometer is schematically illustrated in FIG. 1. The conventional photometer includes a light source 1a, a device for generating monochromatic light 2a, a liquid target 3a, a light sensor 4a, and a display 5a. The light source 1a, device for generating monochromatic light 2a, liquid target 3a, and light sensor 4a are contained within a housing 6a. The display 5a is typically located on an outside surface of the housing 6a. The monochromatic light generally has a spectral bandwidth usually between 0.5 and 10 nm. The device may be a prism, an optical grating or a colour filter (low band-width interference filters or colour filters). This monochromator device can be located either in front or behind the liquid target. The light beam of the conventional photometer is generated by an optical system (lenses or mirrors) from an omnidirectional light source. Typically, the light sensor (e.g. a photo-diode or a photo-multiplier-tube) of the conventional photometer is not capable of distinguishing various colours. More recent devices use multi-CCD (line) detectors, however, the various wavelengths still have to be spatially separated by passing the light-beam through a grating or prism before entering the detector.
The conventional photometer is entirely housed in a single housing 6a. Because of the construction of the conventional photometer, the optics are inward facing. That is, the optics are configured to look within the apparatus toward central chamber in which the sample is placed.